Dynamic anti-windup based control method for state constrained systems

Based on the dynamic anti-windup strategy, an alternative control methodology for state constrained systems is presented. The proposed method is an a posteriori approach for state constrained systems, which is differentiated from the usual a priori approach. That is, first a linear controller is designed to show a desirable nominal performance by ignoring state constraints. Then, an additional compensator is introduced to account for state constraints. By minimizing a reasonable performance index, a dynamic compensator is derived explicitly, which is expressed in plant and controller parameters. The proposed method not only provides a graceful performance degradation, but it also guarantees the total stability of the resulting systems. An illustrative example is given to show the effectiveness of the proposed method.     

Computing isophotos of surface of revolution and canal surface

Isophote of a surface consists of a loci of surface points whose normal vectors form a constant angle with a given fixed vector. It also serves as a silhouette curve when the constant angle is given as π/2. We present efficient and robust algorithms to compute isophotes of a surface of revolution and a canal surface. For the two kinds of surfaces, each point on the isophote is derived by a closed-form solution. To find each connected component in the isophote, we utilize the feature of surface normals. Both surfaces are decomposed into a set of circles, where the surface normal vectors at points on each circle construct a cone. The vectors which form a constant angle with given fixed vector construct another cone. We compute the parametric range of the connected component of the isophote by computing the parametric values of the surface which derive the tangential intersection of these two cones.     

Flank milling with flat end milling cutters

One situation encountered in industry is that two curves on the machined surface are known, such as the top and bottom profiles of a blade. The shape of the surface is not known and is to be determined by a tool sliding along the generating rails. In this paper, we give a detailed mathematical understanding of flank milling with flat end cutters, which we then use to develop a method for milling with such a cutter. This method slides the cutter along two rails, keeping the cutter tangent to both curves at every parameter value. Examples are given to illustrate the method, along with simulations and error analysis.     

Boundary-conformed toolpath generation for trimmed free-form surfaces

In this paper, we adopt a 2D reparameterization procedure to regenerate boundary-conformed toolpaths. Three methods for the 2D reparameterization of trimmed boundaries in parametric space are examined and compared. They are the Coons method, the Laplace method, and a newly developed boundary-blending method. These three methods represent three different approaches to 2D surface parameterization, namely, the algebraic interpolation approach, the partial differential equation approach, and a geometric offsetting approach, respectively. Complete algorithms for surface reparameterization and toolpath generation are developed and implemented. The results showed that the Coons method is relatively simple yet might cause anomalies when the complexities of the boundary are high. The Laplace method is robust but takes relatively more computational time and also has the problem of uneven distribution of iso-parametrics. For the newly developed boundary-blending method, both the computational efficiency and parameterization robustness are quite good, in addition, it alleviates the uneven distribution problem appeared in the Laplace results.     

Computer-aided design method for the components made of heterogeneous materials

With rapid developments of high-tech in various fields, there appear more critical requirements for special functions of components/products, which can be satisfied only by using heterogeneous materials: composite materials, functionally graded materials, or heterogeneous materials with a periodic microstructure. However, currently there exists no systematic and effective method for designing components made of these heterogeneous materials. This paper develops such a computer-aided design method, under the guide of Axiomatic Design, which can apply the functions of current CAD/CAE software. With the design method, all the information about both configuration and materials of a heterogeneous component, needed for creating its CAD model, can be obtained.     

A Web-based collaborative filtering system

In this paper we describe a collaborative filtering system for automatically recommending high-quality information to users with similar interests on arbitrarily narrow information domains. It asks a user to rate a gauge set of items. It then evaluates the user's rates and suggests a recommendation set of items. We interpret the process of evaluation as an inference mechanism that maps a gauge set to a recommendation set. We accomplish the mapping with fuzzy associative memory. We implemented the suggested system in a Web server and tested its performance in the domain of retrieval of technical papers, especially in the field of information technologies. The experimental results show that it may provide reliable recommendations.     

On optimal pairwise linear classifiers for normal distributions: the d-dimensional case

We consider the well-studied pattern recognition problem of designing linear classifiers. When dealing with normally distributed classes, it is well known that the optimal Bayes classifier is linear only when the covariance matrices are equal. This was the only known condition for classifier linearity. In a previous work, we presented the theoretical framework for optimal pairwise linear classifiers for two-dimensional normally distributed random vectors. We derived the necessary and sufficient conditions that the distributions have to satisfy so as to yield the optimal linear classifier as a pair of straight lines.In this paper we extend the previous work to d-dimensional normally distributed random vectors. We provide the necessary and sufficient conditions needed so that the optimal Bayes classifier is a pair of hyperplanes. Various scenarios have been considered including one which resolves the multi-dimensional Minsky’s paradox for the perceptron. We have also provided some three-dimensional examples for all the cases, and tested the classification accuracy of the corresponding pairwise-linear classifier. In all the cases, these linear classifiers achieve very good performance. To demonstrate that the current pairwise-linear philosophy yields superior discriminants on real-life data, we have shown how linear classifiers determined using a maximum-likelihood estimate (MLE) applicable for this approach, yield better accuracy than the discriminants obtained by the traditional Fisher's classifier on a real-life data set. The multi-dimensional generalization of the MLE for these classifiers is currently being investigated.     

The global k-means clustering algorithm

We present the global k-means algorithm which is an incremental approach to clustering that dynamically adds one cluster center at a time through a deterministic global search procedure consisting of N (with N being the size of the data set) executions of the k-means algorithm from suitable initial positions. We also propose modifications of the method to reduce the computational load without significantly affecting solution quality. The proposed clustering methods are tested on well-known data sets and they compare favorably to the k-means algorithm with random restarts.     

Classification of heart rate data using artificial neural network and fuzzy equivalence relation

The electrocardiogram is a representative signal containing information about the condition of the heart. The shape and size of the P-QRS-T wave, the time intervals between its various peaks, etc. may contain useful information about the nature of disease afflicting the heart. However, these subtle details cannot be directly monitored by the human observer. Besides, since bio-signals are highly subjective, the symptoms may appear at random in the time scale. Therefore, the signal parameters, extracted and analysed using computers, are highly useful in diagnostics. This paper deals with the classification of certain diseases using artificial neural network (ANN) and fuzzy equivalence relations. The heart rate variability is used as the base signal from which certain parameters are extracted and presented to the ANN for classification. The same data is also used for fuzzy equivalence classifier. The feedforward architecture ANN classifier is seen to be correct in about 85% of the test cases, and the fuzzy classifier yields correct classification in over 90% of the cases.